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University of Michigan

1. Shnidman, Ariel. Heights of Generalized Heegner Cycles.

Degree: PhD, Mathematics, 2015, University of Michigan

URL: http://hdl.handle.net/2027.42/113442

► We relate the derivative of a p-adic Rankin-Selberg L-function to p-adic heights of the generalized Heegner cycles introduced by Bertolini, Darmon, and *Prasanna*. This generalizes…
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Subjects/Keywords: algebraic cycles; L-functions; arithmetic geometry; number theory; Mathematics; Science

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APA (6^{th} Edition):

Shnidman, A. (2015). Heights of Generalized Heegner Cycles. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/113442

Chicago Manual of Style (16^{th} Edition):

Shnidman, Ariel. “Heights of Generalized Heegner Cycles.” 2015. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/113442.

MLA Handbook (7^{th} Edition):

Shnidman, Ariel. “Heights of Generalized Heegner Cycles.” 2015. Web. 05 Aug 2020.

Vancouver:

Shnidman A. Heights of Generalized Heegner Cycles. [Internet] [Doctoral dissertation]. University of Michigan; 2015. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/113442.

Council of Science Editors:

Shnidman A. Heights of Generalized Heegner Cycles. [Doctoral Dissertation]. University of Michigan; 2015. Available from: http://hdl.handle.net/2027.42/113442

University of Michigan

2. Kaye, Adam Rubin. Arithmetic of the Asai L-function for Hilbert Modular Forms.

Degree: PhD, Mathematics, 2016, University of Michigan

URL: http://hdl.handle.net/2027.42/120693

► Arithmetic of the Asai L-function for Hilbert modular forms Adam Kaye Chair: *Kartik* Prassanna We prove two results on rationality of special values of the…
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Subjects/Keywords: Number Theory; L-functions; Hilbert modular forms; Special values of L-functions; Beilinson's Conjecture; Mathematics; Science

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APA (6^{th} Edition):

Kaye, A. R. (2016). Arithmetic of the Asai L-function for Hilbert Modular Forms. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/120693

Chicago Manual of Style (16^{th} Edition):

Kaye, Adam Rubin. “Arithmetic of the Asai L-function for Hilbert Modular Forms.” 2016. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/120693.

MLA Handbook (7^{th} Edition):

Kaye, Adam Rubin. “Arithmetic of the Asai L-function for Hilbert Modular Forms.” 2016. Web. 05 Aug 2020.

Vancouver:

Kaye AR. Arithmetic of the Asai L-function for Hilbert Modular Forms. [Internet] [Doctoral dissertation]. University of Michigan; 2016. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/120693.

Council of Science Editors:

Kaye AR. Arithmetic of the Asai L-function for Hilbert Modular Forms. [Doctoral Dissertation]. University of Michigan; 2016. Available from: http://hdl.handle.net/2027.42/120693

University of Michigan

3. Pal, Suchandan. p-adic Uniformization and an Explicit Jacquet-Langlands Isomorphism.

Degree: PhD, Mathematics, 2016, University of Michigan

URL: http://hdl.handle.net/2027.42/133472

► In this thesis, we study modular forms on definite and indefinite quaternion algebras. These spaces are a priori very different. On the definite side they…
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Subjects/Keywords: An Explicit Jacquet-Langlands Isomorphism; Mathematics; Science

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APA (6^{th} Edition):

Pal, S. (2016). p-adic Uniformization and an Explicit Jacquet-Langlands Isomorphism. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/133472

Chicago Manual of Style (16^{th} Edition):

Pal, Suchandan. “p-adic Uniformization and an Explicit Jacquet-Langlands Isomorphism.” 2016. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/133472.

MLA Handbook (7^{th} Edition):

Pal, Suchandan. “p-adic Uniformization and an Explicit Jacquet-Langlands Isomorphism.” 2016. Web. 05 Aug 2020.

Vancouver:

Pal S. p-adic Uniformization and an Explicit Jacquet-Langlands Isomorphism. [Internet] [Doctoral dissertation]. University of Michigan; 2016. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/133472.

Council of Science Editors:

Pal S. p-adic Uniformization and an Explicit Jacquet-Langlands Isomorphism. [Doctoral Dissertation]. University of Michigan; 2016. Available from: http://hdl.handle.net/2027.42/133472

University of Michigan

4. Ormsby, Kyle M. Computations in Stable Motivic Homotopy Theory.

Degree: PhD, Mathematics, 2010, University of Michigan

URL: http://hdl.handle.net/2027.42/77824

► This thesis is concerned with the application of certain computational methods from stable algebraic topology in motivic homotopy theory over p-adic fields. My main tools…
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Subjects/Keywords: Motivic Homotopy; Stable Homotopy; Adams-Novikov Spectral Sequence; Algebraic K-theory; Algebraic Cobordism; Mathematics; Science

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APA (6^{th} Edition):

Ormsby, K. M. (2010). Computations in Stable Motivic Homotopy Theory. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/77824

Chicago Manual of Style (16^{th} Edition):

Ormsby, Kyle M. “Computations in Stable Motivic Homotopy Theory.” 2010. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/77824.

MLA Handbook (7^{th} Edition):

Ormsby, Kyle M. “Computations in Stable Motivic Homotopy Theory.” 2010. Web. 05 Aug 2020.

Vancouver:

Ormsby KM. Computations in Stable Motivic Homotopy Theory. [Internet] [Doctoral dissertation]. University of Michigan; 2010. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/77824.

Council of Science Editors:

Ormsby KM. Computations in Stable Motivic Homotopy Theory. [Doctoral Dissertation]. University of Michigan; 2010. Available from: http://hdl.handle.net/2027.42/77824

5. Hyde, Trevor. Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture.

Degree: PhD, Mathematics, 2019, University of Michigan

URL: http://hdl.handle.net/2027.42/151684

► This thesis consists of six chapters representing two directions of the author’s graduate research under the advisement of Jeffrey Lagarias and Michael Zieve. The first…
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Subjects/Keywords: Configuration space; Necklace polynomial; Dynamical Mordell-Lang; Mathematics; Science

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APA (6^{th} Edition):

Hyde, T. (2019). Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/151684

Chicago Manual of Style (16^{th} Edition):

Hyde, Trevor. “Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture.” 2019. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/151684.

MLA Handbook (7^{th} Edition):

Hyde, Trevor. “Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture.” 2019. Web. 05 Aug 2020.

Vancouver:

Hyde T. Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture. [Internet] [Doctoral dissertation]. University of Michigan; 2019. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/151684.

Council of Science Editors:

Hyde T. Polynomial Statistics, Necklace Polynomials, and the Arithmetic Dynamical Mordell-Lang Conjecture. [Doctoral Dissertation]. University of Michigan; 2019. Available from: http://hdl.handle.net/2027.42/151684

6. Carter, Brandon. Jochnowitz Congruences at Residual Primes.

Degree: PhD, Mathematics, 2018, University of Michigan

URL: http://hdl.handle.net/2027.42/145998

► We investigate relationships between the algebraic parts of L-values of weight two eigenforms f and g satisfying a congruence modulo a prime p, but whose…
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Subjects/Keywords: Arithmetic geometry; Mathematics; Science

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APA (6^{th} Edition):

Carter, B. (2018). Jochnowitz Congruences at Residual Primes. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/145998

Chicago Manual of Style (16^{th} Edition):

Carter, Brandon. “Jochnowitz Congruences at Residual Primes.” 2018. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/145998.

MLA Handbook (7^{th} Edition):

Carter, Brandon. “Jochnowitz Congruences at Residual Primes.” 2018. Web. 05 Aug 2020.

Vancouver:

Carter B. Jochnowitz Congruences at Residual Primes. [Internet] [Doctoral dissertation]. University of Michigan; 2018. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/145998.

Council of Science Editors:

Carter B. Jochnowitz Congruences at Residual Primes. [Doctoral Dissertation]. University of Michigan; 2018. Available from: http://hdl.handle.net/2027.42/145998

7. Kopp, Gene. Indefinite Theta Functions and Zeta Functions.

Degree: PhD, Mathematics, 2017, University of Michigan

URL: http://hdl.handle.net/2027.42/140957

► We define an indefinite theta function in dimension g and index 1 whose modular parameter transforms by a symplectic group, generalizing a construction of Sander…
(more)

Subjects/Keywords: number theory; indefinite theta function; zeta function; real quadratic field; Kronecker limit formula; SIC-POVM; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Kopp, G. (2017). Indefinite Theta Functions and Zeta Functions. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/140957

Chicago Manual of Style (16^{th} Edition):

Kopp, Gene. “Indefinite Theta Functions and Zeta Functions.” 2017. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/140957.

MLA Handbook (7^{th} Edition):

Kopp, Gene. “Indefinite Theta Functions and Zeta Functions.” 2017. Web. 05 Aug 2020.

Vancouver:

Kopp G. Indefinite Theta Functions and Zeta Functions. [Internet] [Doctoral dissertation]. University of Michigan; 2017. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/140957.

Council of Science Editors:

Kopp G. Indefinite Theta Functions and Zeta Functions. [Doctoral Dissertation]. University of Michigan; 2017. Available from: http://hdl.handle.net/2027.42/140957

8. Scherr, Zachary L. Rational Polynomial Pell Equations.

Degree: PhD, Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/100026

► Let R denote either the integers or the rationals and let d(x) be a square-free polynomial in R[x]. In this thesis we study the question…
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Subjects/Keywords: Number Theory; Polynomial Pell Equations; Mathematics; Science

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APA (6^{th} Edition):

Scherr, Z. L. (2013). Rational Polynomial Pell Equations. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/100026

Chicago Manual of Style (16^{th} Edition):

Scherr, Zachary L. “Rational Polynomial Pell Equations.” 2013. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/100026.

MLA Handbook (7^{th} Edition):

Scherr, Zachary L. “Rational Polynomial Pell Equations.” 2013. Web. 05 Aug 2020.

Vancouver:

Scherr ZL. Rational Polynomial Pell Equations. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/100026.

Council of Science Editors:

Scherr ZL. Rational Polynomial Pell Equations. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/100026

9. Brooks, Ernest Hunter. Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions.

Degree: PhD, Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/99928

► We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the…
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Subjects/Keywords: Algebraic Number Theory; Mathematics; Science

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APA (6^{th} Edition):

Brooks, E. H. (2013). Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/99928

Chicago Manual of Style (16^{th} Edition):

Brooks, Ernest Hunter. “Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions.” 2013. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/99928.

MLA Handbook (7^{th} Edition):

Brooks, Ernest Hunter. “Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions.” 2013. Web. 05 Aug 2020.

Vancouver:

Brooks EH. Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/99928.

Council of Science Editors:

Brooks EH. Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/99928

10. Rosen, Julian H. The Arithmetic of Multiple Harmonic Sums.

Degree: PhD, Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/99893

► This dissertation concerns the arithmetic of a family of rational numbers called multiple harmonic sums. These sums are finite truncations of multiple zeta values. We…
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Subjects/Keywords: Multiple Harmonic Sums; Mathematics; Science

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APA (6^{th} Edition):

Rosen, J. H. (2013). The Arithmetic of Multiple Harmonic Sums. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/99893

Chicago Manual of Style (16^{th} Edition):

Rosen, Julian H. “The Arithmetic of Multiple Harmonic Sums.” 2013. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/99893.

MLA Handbook (7^{th} Edition):

Rosen, Julian H. “The Arithmetic of Multiple Harmonic Sums.” 2013. Web. 05 Aug 2020.

Vancouver:

Rosen JH. The Arithmetic of Multiple Harmonic Sums. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/99893.

Council of Science Editors:

Rosen JH. The Arithmetic of Multiple Harmonic Sums. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/99893

11. Ngo, Hieu T. Generalizations of the Lerch zeta function.

Degree: PhD, Mathematics, 2014, University of Michigan

URL: http://hdl.handle.net/2027.42/108812

► The Lerch zeta function is a three-variable generalization of the Riemann zeta function and the Hurwitz zeta function. In this thesis, we study generalizations and…
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Subjects/Keywords: Number Theory; Mathematics; Science

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APA (6^{th} Edition):

Ngo, H. T. (2014). Generalizations of the Lerch zeta function. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/108812

Chicago Manual of Style (16^{th} Edition):

Ngo, Hieu T. “Generalizations of the Lerch zeta function.” 2014. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/108812.

MLA Handbook (7^{th} Edition):

Ngo, Hieu T. “Generalizations of the Lerch zeta function.” 2014. Web. 05 Aug 2020.

Vancouver:

Ngo HT. Generalizations of the Lerch zeta function. [Internet] [Doctoral dissertation]. University of Michigan; 2014. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/108812.

Council of Science Editors:

Ngo HT. Generalizations of the Lerch zeta function. [Doctoral Dissertation]. University of Michigan; 2014. Available from: http://hdl.handle.net/2027.42/108812

12. Sun, Xinyun. CM p-divisible Groups over Finite Fields.

Degree: PhD, Mathematics, 2011, University of Michigan

URL: http://hdl.handle.net/2027.42/84531

► The primary motivation for this dissertation is to further the study of CM lifting of abelian varieties based on work by Chai, Conrad, and Oort.…
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Subjects/Keywords: CM P-divisible Group; Mathematics; Science

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APA (6^{th} Edition):

Sun, X. (2011). CM p-divisible Groups over Finite Fields. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/84531

Chicago Manual of Style (16^{th} Edition):

Sun, Xinyun. “CM p-divisible Groups over Finite Fields.” 2011. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/84531.

MLA Handbook (7^{th} Edition):

Sun, Xinyun. “CM p-divisible Groups over Finite Fields.” 2011. Web. 05 Aug 2020.

Vancouver:

Sun X. CM p-divisible Groups over Finite Fields. [Internet] [Doctoral dissertation]. University of Michigan; 2011. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/84531.

Council of Science Editors:

Sun X. CM p-divisible Groups over Finite Fields. [Doctoral Dissertation]. University of Michigan; 2011. Available from: http://hdl.handle.net/2027.42/84531

13. Jia, Johnson X. Arithmetic of the Yoshida Lift.

Degree: PhD, Mathematics, 2010, University of Michigan

URL: http://hdl.handle.net/2027.42/77876

► Co-Chairs: Stephen M. DeBacker and Christopher M. Skinner This thesis concerns the arithmetic properties of the Yoshida lift, Y, which is a scalar- valued holomorphic…
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Subjects/Keywords: Yoshida Lift; Theta Lifts; Automorphic Forms; Non-vanishing; GSp_4; Integrality; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Jia, J. X. (2010). Arithmetic of the Yoshida Lift. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/77876

Chicago Manual of Style (16^{th} Edition):

Jia, Johnson X. “Arithmetic of the Yoshida Lift.” 2010. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/77876.

MLA Handbook (7^{th} Edition):

Jia, Johnson X. “Arithmetic of the Yoshida Lift.” 2010. Web. 05 Aug 2020.

Vancouver:

Jia JX. Arithmetic of the Yoshida Lift. [Internet] [Doctoral dissertation]. University of Michigan; 2010. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/77876.

Council of Science Editors:

Jia JX. Arithmetic of the Yoshida Lift. [Doctoral Dissertation]. University of Michigan; 2010. Available from: http://hdl.handle.net/2027.42/77876

14. Chan, Charlotte. Period Identities of CM Forms on Quaternion Algebras.

Degree: PhD, Mathematics, 2018, University of Michigan

URL: http://hdl.handle.net/2027.42/145838

► A few decades ago, Waldspurger proved a groundbreaking identity between the central value of an L-function and the norm of a torus period. Combining this…
(more)

Subjects/Keywords: automorphic forms; torus periods; theta lifts; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Chan, C. (2018). Period Identities of CM Forms on Quaternion Algebras. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/145838

Chicago Manual of Style (16^{th} Edition):

Chan, Charlotte. “Period Identities of CM Forms on Quaternion Algebras.” 2018. Doctoral Dissertation, University of Michigan. Accessed August 05, 2020. http://hdl.handle.net/2027.42/145838.

MLA Handbook (7^{th} Edition):

Chan, Charlotte. “Period Identities of CM Forms on Quaternion Algebras.” 2018. Web. 05 Aug 2020.

Vancouver:

Chan C. Period Identities of CM Forms on Quaternion Algebras. [Internet] [Doctoral dissertation]. University of Michigan; 2018. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2027.42/145838.

Council of Science Editors:

Chan C. Period Identities of CM Forms on Quaternion Algebras. [Doctoral Dissertation]. University of Michigan; 2018. Available from: http://hdl.handle.net/2027.42/145838